Magnetic resonance imaging (MRI) apparatus is apparatus that visualizes internal body information of a subject utilizing a nuclear magnetic resonance phenomenon. MRI apparatus uses coils to collect data called k-space data by sampling nuclear resonance signals from specific atomic nuclei (e.g., atomic nuclei of hydrogen atoms) in a subject and applies Fourier transform to the k-space data to obtain magnetic resonance (MR) images.
The nuclear resonance signals are sampled as one dimensional data. The MRI apparatus collects data necessary to produce two-dimensional or three-dimensional MR images by repeating one dimensional sampling in a k-space. When the k-space data is sampled with the same resolution (full sampling) as the MR image to be output, the MR image can be produced by applying Fourier transform to the acquired k-space data.
It is known that the MRI apparatuses take time to perform the sampling. If it takes time to perform the sampling in capturing time-series data using the MRI apparatus, an imaging speed is reduced. As a result, imaging cannot follow the movement of the subject. Various techniques to achieve high speed imaging have been researched and developed. One of such techniques is called parallel imaging (PI). In the parallel imaging, the k-space data is collected using a sampling pattern (undersampling) whose number of samples is smaller than that of full sampling and a plurality of coils. When Fourier transform is applied to the k-space data after the undersampling without any change, aliasing occurs. In the parallel imaging, the MR image having no aliasing caused by the undersampling is produced using a difference in sensitivity caused by the geometrical arrangement of the coils.
The following describes a procedure of sensitivity encoding (SENSE), which is one form of the parallel imaging. Information about a sensitivity distribution of each coil is collected in advance by a reference scan, for example. The MRI apparatus, then, performs Fourier transform using the undersampled k-space data of the respective coils obtained by image scan to generate the MR images in relation to the respective coils. Thereafter, the MRI apparatus estimates a true MR image on the basis of a premise that the MR images in relation to the respective coils are images obtained by performing, on the true MR image, product-sum operation of the sensitivity distribution information of the respective coils and aliased signals of the respective coils.
In k-t SENSE, which is one form of the extended SENSE, aliasing is removed by the SENSE in a space where Fourier transform is applied to the time-series MR images on a temporal axis. In the parallel imaging, a value obtained by dividing the number of samples in the full sampling by the number of samples in the undersampling is called a reduction factor R. In the SENSE and the extended SENSE techniques, the sampling is often performed at the same intervals in the k-space so as to remove the aliasing with a small amount of computation.
In the SENSE and the k-t SENSE, the larger the reduction factor R is, the larger a reconstruction noise is. As techniques to reduce the reconstruction noise, techniques such as regularization and compressed sensing that use prior knowledge are known. The reduction of the large reconstruction noise needs to increase dependency on such prior knowledge. As a result, the obtained MR image is strongly influenced by the prior knowledge given in the regularization. Especially, reproducibility of detailed structure in the obtained MR image is damaged.